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nLab > Latest Changes: globular set

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  1. I added a reference to globular set.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2012

    I have edited globular set a little, trying to prettyfie the exposition mainly. Also added another line or two to the Idea-section and added another reference.

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 18th 2019

    Is anything known about globular sets in terms of Grothendieck homotopy theory? For instance, is the category of globes a weak test category, a test category, or a strict test category?

  4. I’m pretty sure it is provably not a test category. Just now I’m not sure of a reference, I’ll see if I can remember one later.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeMar 19th 2019

    That’s what I thought I remembered too, but I don’t know the reference either. My intuition is that the boundary of a globular set is “too simple to encode composition” the way (say) simplices and cubes do.

    • CommentRowNumber6.
    • CommentAuthorUlrik
    • CommentTimeMar 19th 2019

    This is discussed in Scholie 8.4.14 in Cisinski’s Astérisque 308.

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 20th 2019
    • (edited Mar 20th 2019)

    Added remarks about the Grothendieck homotopy theory of globes and polyglobes.

    diff, v34, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 20th 2019

    Added remarks about the Grothendieck homotopy theory of globes and polyglobes.

    diff, v34, current

    • CommentRowNumber9.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 20th 2019

    Trying to add the same material for the third time, it keeps disappearing. What is going on?

    diff, v34, current

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 20th 2019

    Something is seriously broken on the nLab. It appears that new edits edit the second-to-the-last version instead of the latest one!

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 29th 2023
    • (edited Mar 29th 2023)

    What exactly does this article mean by this sentence:

    They are one of the major geometric shapes for higher structures: if they satisfy a globular Segal condition then they are equivalent to strict ∞-categories.

    What is the “globular Segal condition”? I thought we need to pass from the category of globes to the category Theta_n to formulate such a Segal condition?

    (Added by Urs on November 6, 2012 in Revision 24.)

    diff, v37, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2023

    Thanks for highlighting. That sentence didn’t make good sense. I have replaced it by:

    Globular sets have been used as a geometric shape for higher structures: when equipped with suitable composition operation on their cells they model a notion of strict ∞-categories.

    diff, v38, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2023
    • (edited Mar 29th 2023)

    I have further expanded that sentence on relation to models for higher catgeories, adding pointer also to associative n-categories.

    And so I now gave the paragraph its own subsection: “Properties – As shapes for higher categories” (now here).

    diff, v39, current

1 to 13 of 13

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